Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions (2007.03528v2)

Abstract: We show that if $A\subset {1,\ldots,N}$ contains no non-trivial three-term arithmetic progressions then $\lvert A\rvert \ll N/(\log N)^{1+c}$ for some absolute constant $c>0$. In particular, this proves the first non-trivial case of a conjecture of Erd\H{o}s on arithmetic progressions.